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Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China

Vortex dynamics is at the heart of many unresolved problems in fluid mechanics and is also central to numerous applications in science and engineering. The goal of the proposed meeting is to survey the recent progress in this field focusing on applied mathematics aspects of both classical and emerging problems. We are planning to bring together about 40 researchers at different career stages working on various aspects of vortex dynamics, spanning applied mathematical analysis, scientific computing, physical modeling as well as scientific and engineering applications. A highlight of the workshop will be events designed to foster cross-fertilization between applied mathematics and different application areas.

Institute for Advanced Study in Mathematics (IASM)

The theories of rational/trigonometric/elliptic functions were developed as functions over plane/cylinder/torus, respectively, before the 20th century. Among them, the theory of elliptic functions is most interesting, and it can be understood as the parent theory of the rest. During the 20th century, the same rational/trigonometric/elliptic trichotomy has been also found in integrable systems, algebras and cohomology groups. Like the theory of functions, recent development reveals that the relationship among integrable system, algebra, geometry, and physics becomes most profound at elliptic level. In particular, Lie algebras (rational) are promoted to affine Lie algebras (trigonometric) and toroidal Lie algebras (elliptic). The workshop aims at investigating quantum versions of toroidal Lie algebras, called quantum toroidal algebras.

Algebra,    Geometry and Topology

Institute for Advanced Study in Mathematics (IASM)

This symposium brings together mathematicians, computer scientists, chemists and physicist to address a truly multidisciplinary issue of enabling large-scale atomistically-resolved, ab initio materials modeling. Such modeling capabilities are required for understanding and rational design of materials ranging from alloys to solid electrolytes for fuel cells. There is a substantial gap in theory and computing techniques which on one hand would be able to model phenomena intrinsically requiring models with millions of atoms and on the other hand provide accuracy and insight which is today routinely achievable only for unrealistically small model systems . This is a gap between a model and a reality. To bridge it, this symposium makes brains from different research fields pull in one direction. Progress that this symposium will help accelerate will mean better computational support for the development of functional materials, with more of the development moved from time-, manpower-, and $-costly lab experimentation to in-silico design.

Condensed Matter Physics and Materials,    Computational Physics and Numerical Simulation

Institute for Advanced Study in Mathematics (IASM)

Nonlinear problems are problems which solutions satisfy an equation where the different physical constants involved are depending on the solution itself. This dependence can be nonlocal in the sense that it depends on the solution globally. For instance the motion of a population can be influenced by the total population and not only by the population very locally. One of the goals of the workshop is to deepen the human knowledge in this field applied to different situations.